Subspaces spanned by eigenforms with nonvanishing twisted central $L$-values
Number Theory
2024-07-02 v1
Abstract
In this paper, we construct explicit spanning sets for two spaces. One is the subspace generated by integral-weight Hecke eigenforms with nonvanishing quadratic twisted central -values. The other is a subspace generated by half-integral weight Hecke eigenforms with certain nonvanishing Fourier coefficients. Along the way, we show that these subspaces are isomorphic via the Shimura lift.
Cite
@article{arxiv.2407.00532,
title = {Subspaces spanned by eigenforms with nonvanishing twisted central $L$-values},
author = {June Kayath and Connor Lane and Ben Neifeld and Tianyu Ni and Hui Xue},
journal= {arXiv preprint arXiv:2407.00532},
year = {2024}
}
Comments
38 pages